Some time ago, Language Log discussed a language usage in the web comic Dumbing of Age by David Willis. Since then I have been reading it every day. One recent daily strip has one character saying, in her idiolect, “Ah still don’t ever tell no authority figures nothing”.

(Don’t worry about who these people are and what they’re talking about.)
Proscriptivists proscribe double negatives because, logically, two negatives make a positive. “I didn’t do nothing” means I did something. But no-one ever said it to mean that, and no-one ever seriously understands it to mean that. They don’t prescribe triple negatives, even though, logically, three negatives make a positive. “I didn’t do nothing to nobody” means I did something to nobody.
Language isn’t logic or mathematics. For those people who use double negatives of this kind (of which I am not one), it isn’t negative times negative equals positive, but rather negative plus negative equals negative (which is equally logical and mathematical). Triple negatives don’t attract as much comment because they are so much rarer. Some languages require double negatives. I don’t know whether, in those languages, single negatives are a non-standard option or just plain wrong.
A few days ago I posted something on Facebook about a recent international event. My wife asked me about it and I said “No-one’s disagreed with me”. I had to explain that this is not the same as saying “Someone’s agreed with me”.